Using 980 fb-1 of data collected on and around the (nS) (n=1, 2, 3, 4, 5) resonances with the Belle detector at the KEKB collider, we measure the cross section of e+e-→ηφ from threshold to 3.95 GeV via initial state radiation. There are clear φ(1680) and J/ψ signals but no significant φ(2170) signal in the ηφ final state. The branching fraction B[J/ψ→ηφ] is measured to be (7.2±0.8±0.5)×10-4. The resonant parameters of φ(1680) are determined to be mφ(1680)=(1696±8±10) MeV/c2 (statistical and systematic errors, respectively), Γφ(1680)=(175±13±16) MeV and, depending on the possible presence of predominantly constructive or destructive interference between φ(1680) and continuum production, Γφ(1680)e+e-·B[φ(1680)→ηφ] and B[φ(1680)→ηφ] are determined to be (75±10±11) eV and (25±12±2)% or (207±16±20) eV and (23±10±2)%, respectively. The upper limit for Γφ(2170)e+e-·B[φ(2170)→ηφ] is determined to be either 0.17 or 18.6 eV at the 90% confidence level.